Q5. (15 pts) Use RSA to encrypt and decrypt back m=4 if N=77. Define yourself all necessary ingredients of RSA, give necessary explanations. Hint: RSA (Rivest-Shamir-Adelman, 1978) algorithm is an asymmetric encryption algorithm. To design an encryption/decryption key pair, two large prime numbers, p and q, p#q, are selected, and an integer, e, is chosen that is relatively prime to (p-1)(q-1) (e and (p-1)(2-1) have no common factors other than 1). Finally, an integer d is computed such that ed=1(mod(p-1)(9-1)) One key is (e, N), and the other key is (d, N), where N=p*q, and is referred to as the modulus. For example, We might select p=7, and q=13. Then N=p*q=91, and (p-1)(4-1)= 72. We can choose e=5 (which is relatively prime to 72) and d=29, because e*d=145 and 145 = 1(mod 72) Then, one key is K1=(e, N)=(5,91) and the other key is K2=(d, N)=(29,91). The message (plaintext) to be encrypted is broken into blocks such that each block, M, can be treated as an integer between 0 and (N-1). To encrypt M into the ciphertext block, C, we perform C = M mod N To decrypt C, we perform M=C'mod N